Latest Papers

Based on the interaction between the radiation field and a superconductor, we propose a way to engineer quantum states using a SQUID charge qubit inside a microcavity. This device can act as a deterministic single photon source as well as generate any Fock states and an arbitrary superposition of Fock states for the cavity field. The controllable interaction between the cavity field and the qubit can be realized by the tunable gate voltage and classical magnetic field applied to the SQUID.

A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schrödinger matrix Hamiltonians is characterized. The applications are oriented towards the Jaynes-Cummings eigenvalue problem, so that exactly solvable $2\times 2$ matrix Hamiltonians of the Jaynes-Cummings type are obtained. It is also established that the Jaynes-Cummings Hamiltonian is a quadratic function of a Dirac-type Hamiltonian.

This report presents an approach to the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without the rotating wave approximation (RWA). It is shown that there is a squeezing-operator unitary transformation for relating the J-C model without RWA and the one with RWA. Thus by using an appropriate squeezing unitary transformation, the time-dependent J-C model without RWA can be transformed into the one with RWA that has been exactly solved previously, and based on this one can readily obtain the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without RWA. The approach presented here also shows that we can treat these two kinds of time-dependent J-C models (both with and without RWA) in a unified way.

We present a multi-level quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external impedances, shunt resistors) are described using the Caldeira-Leggett model. The master equation for the superconducting phases in the Born-Markov approximation is derived and brought into the Bloch-Redfield form in order to describe multi-level dissipative quantum dynamics of the circuit. The model takes into account leakage effects, i.e. transitions from the allowed qubit states to higher excited states of the system. As a special case, we truncate the Hilbert space and derive a two-level (Bloch) theory with characteristic relaxation (T_1) and decoherence (T_2) times. We apply our theory to the class of superconducting flux qubits; however, the formalism can be applied for both superconducting flux and charge qubits.

We propose a scheme to physically interface superconducting nano-circuits and quantum optics. We address the transfer of quantum information between systems having different physical natures and defined in Hilbert spaces of different dimensions. In particular, we investigate the transfer of the entanglement initially in a non-classical state of a continuous-variable system to a pair of superconducting charge qubits. This set-up is able to drive an initially separable state of the qubits into an almost pure, highly entangled state suitable for quantum information processing.

We combine the ideas of qubit encoding and dispersive dynamics to enable robust and easy quantum information processing (QIP) on paired superconducting charge boxes sharing a common bias lead. We establish a decoherence free subspace on these and introduce universal gates by dispersive interaction with a LC resonator and inductive couplings between the encoded qubits. These gates preserve the code space and only require the established local symmetry and the control of the voltage bias.

Two of the major obstacles to achieve quantum computing (QC) are (i) scalability to many qubits and (ii) controlled connectivity between any selected qubits. Using Josephson charge qubits, here we propose an experimentally realizable method to efficiently solve these two central problems. Since any two charge qubits can be effectively coupled by an experimentally accessible inductance, the proposed QC architecture is scalable. In addition, we formulate an efficient and realizable QC scheme that requires only one (instead of two or more) two-bit operation to implement conditional gates.

We investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field. We demonstrate the existence of Rabi oscillations for both single- and multi-photon processes and, moreover, we propose a new quantum computing scheme (including one-bit and conditional two-bit gates) based on Josephson qubits coupled through microwaves.

By using both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside the optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses the supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schrödinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories.

It is usually argued that the presence of gapless quasiparticle excitations at the nodes of the d-wave superconducting gap should strongly decohere the quantum states of a d-wave qubit, making quantum effects practically unobservable. Using a self-consistent linear response non-equilibrium quasiclassical formalism, we show that this is not necessarily true. We find quasiparticle conductance of a d-wave grain boundary junction to be strongly phase dependent. Midgap states as well as nodal quasiparticles contribute to the conductance and therefore decoherence. Quantum behavior is estimated to be detectable in a qubit containing a d-wave junction with appropriate parameters.

Superconducting, flux-based qubits are promising candidates for the construction of a large scale quantum computer. We present an explicit quantum mechanical calculation of the coherent behavior of a flux based quantum bit in a noisy experimental environment such as an integrated circuit containing bias and control electronics. We show that non-thermal noise sources, such as bias current fluctuations and magnetic coupling to nearby active control circuits, will cause decoherence of a flux-based qubit on a timescale comparable to recent experimental coherence time measurements.

A quantum-mechanical model for the interaction of Josephson vortices (fluxons) embedded in superconducting transmission line is presented. The vortices interact through emission and absorption of linear waves (electromagnetic cavity modes). We show that in a classical regime this peculiar type of interaction is determined by the product of instantaneous velocities of fluxons. In a quantum regime, this property provides tunable coupling between vortices which can be used for entanglement of vortex qubits. The physical mechanism of the vortex interaction is similar to that proposed for qubits based on trapped ions. Different types of transmission lines mediating the vortex interaction are proposed.

Interaction of a two-level atom with a single mode of electromagnetic field including Kerr nonlinearity for the field and intensity-dependent atom-field coupling is discussed. The Hamiltonian for the atom-field system is written in terms of the elements of a closed algebra, which has SU(1,1) and Heisenberg-Weyl algebras as limiting cases. Eigenstates and eigenvalues of the Hamiltonian are constructed. With the field being in a coherent state initially, the dynamical behaviour of atomic-inversion, field-statistics and uncertainties in the field quadratures are studied. The appearance of nonclassical features during the evolution of the field is shown. Further, we explore the overlap of initial and time-evolved field states.

An exact density matrix of a phase-damped Jaynes - Cummings model (JCM) with entangled Bell-like initial states formed from a model two-state atom and sets of adjacent photon number states of a single mode radiation field is presented. The entanglement of the initial states and the subsequent time evolution is assured by finding a positive lower bound on the concurrence of local 2x2 projections of the full 2xinfinity JCM density matrix. It is found that the time evolution of the lower bound of the concurrence systematically captures the corresponding collapse and revival features in atomic inversion, relative entropies of atomic and radiation, mutual entropy, and quantum deficit. The atom and radiation subsystems exhibit alternating sets of collapses and revivals in a complementary fashion due to the initially mixed states of the atom and radiation employed here. This is in contrast with the result obtained when the initial state of the dissipationless system is a factored pure state of atom and radiation, where the atomic and radiation entropies are necessarily the same. The magnitudes of the entanglement lower bound and the atomic and radiation revivals become larger as both magnitude and phase of the Bell-like initial state contribution increases. The time evolution of the entropy difference of the total system and that of the radiation subsystem exhibits negative regions called "supercorrelated" states which do not appear in the atomic subsystem. Entangled initial states are found to enhance this supercorrelated feature. Finally, the effect of phase damping is to randomize both the subsystems for asymptotically long times .

We give a fully description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom-field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any initial state and we show that atom-field steady state is at most classically correlated. For an initial state chosen, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. Moreover, we show that the degree of entanglement of the atom-field state, for the particular initial state chosen, can be completely quantified by concurrence. Analytical expression for time evolution of the concurrence is given.

We propose to subject two Bose-Einstein condensates to a periodic potential, so that one condensate undergoes the Mott insulator transition to a state with precisely one atom per lattice site. We show that photoassociation of heteronuclear molecules within each lattice site is described by the quantum optical Jaynes-Cummings Hamiltonian. In analogy with studies of this Hamiltonian with cavity fields and trapped ions, we are thus able to engineer quantum optical states of atomic matter wave fields and we are able to reconstruct these states by quantum state tomography.

We describe a mathematical solution for the generation of entangled N-photon states in two field modes. A simple and compact solution is presented for a two-mode Jaynes-Cummings model by combining the two field modes in a way that only one of the two resulting quasi-modes enters in the interaction term. The formalism developed is then applied to calculate various generation probabilities analytically. We show that entanglement, starting from an initial field and an atom in one defined state may be obtained in a single step. We also show that entanglement may be built up in the case of an empty cavity and excited atoms whose final states are detected, as well as in the case when the final states of the initially excited atoms are not detected.

A unitary transformation of the N-ion Jaynes-Cummings hamiltonian is proposed. It is shown that any approximate expression of the evolution operator associated with the transformed hamiltonian retains its validity independently from the intensity of the external driving field. In particular, using the rotating wave approximation, one obtains a solution for the N-ion Jaynes-Cummings model which improves the standard rotating wave approximation solution.

We study an LC-circuit implemented using a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias current, the junction can be tuned in and out of resonance and entangled with the qubits coupled to it. One can thus implement two-qubit operations by mediating entanglement. We consider the examples of CBJJ and charge--phase qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit designs.

We present a propagator formalism to investigate the scattering of photons by a cavity QED system that consists of a single two-level atom dressed by a leaky optical cavity field. We establish a diagrammatic method to construct the propagator analytically. This allows us to determine the quantum state of the scattered photons for an arbitrary incident photon packet. As an application, we explicitly solve the problem of a single-photon packet scattered by an initially excited atom.